few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Mathematical concept/skill options: 
A. Write expressions in equivalent forms to solve problems.
B. Understand properties of multiplication and the relationship between multiplication and division.
C. Interpret the structure of expressions.
D. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
E. Use polynomial identities to solve problems.
F. Understand the relationship between zeros and factors of polynomials.
G. Write and interpret numerical expressions.
H. Work with equal groups of objects to gain foundations for multiplication.
I. Perform arithmetic operations on polynomials.
J. Create equations that describe numbers or relationships
K. Generate and analyze patterns.
L. Analyze and solve linear equations and pairs of simultaneous linear equations.
M. Understand solving equations as a process of reasoning and explain the reasoning.
N. Apply and extend previous understandings of arithmetic to algebraic expressions.
O. Rewrite rational expressions.
P. Represent and solve problems involving multiplication and division.
Q. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
R. Reason about and solve one-variable equations and inequalities.
S. Understand and apply properties of operations and the relationship between addition and subtraction.
T. Understand the connections between proportional relationships, lines, and linear equations.
U. Multiply and divide within 100.
V. Gain familiarity with factors and multiples.
W. Use the four operations with whole numbers to solve problems.
X. Work with addition and subtraction equations.
Y. Represent and solve problems involving addition and subtraction.
Z. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
AA. Solve equations and inequalities in one variable.
AB. Solve systems of equations.
AC. Represent and analyze quantitative relationships between dependent and independent variables.
AD. Work with radicals and integer exponents.
AE. Represent and solve equations and inequalities graphically.
AF. Analyze patterns and relationships.
AG. Use properties of operations to generate equivalent expressions.
AH. Add and subtract within 20.


Thought: This set of problems involves solving linear equations and pairs of linear equations.
Answer: L

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001392

8
options: Visualize relationships between two-dimensional and three-dimensional objects.

Reason with shapes and their attributes.

Find arc lengths and areas of sectors of circles.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Understand similarity in terms of similarity transformations.

Understand congruence in terms of rigid motions.

Solve real-world and mathematical problems involving area, surface area, and volume.

Explain volume formulas and use them to solve problems.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Understand and apply theorems about circles.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

Classify two-dimensional figures into categories based on their properties.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Use coordinates to prove simple geometric theorems algebraically.

Apply trigonometry to general triangles.

Apply geometric concepts in modeling situations.

Experiment with transformations in the plane.

Understand and apply the Pythagorean Theorem.

Analyze, compare, create, and compose shapes.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Make geometric constructions.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Prove geometric theorems.

Translate between the geometric description and the equation for a conic section.
problem_activity: Problem 1
Geraldo is plotting points on the following coordinate plane.
[IMG]
Geraldo needs to plot the following four points:
(0.8, 12)
(1.6, 18)
(1, 30)
(2, 3)
Can he plot all of his points on the provided coordinate plane? How do you know?
What would be a point that he couldn't fit on the coordinate plane above? How do you know?
Problem 2
Determine the correct scale for the coordinate grid below so that all of the following points can be shown on it:
(12, 4)
(4,
$${1\over2}$$
)
(6,
$$3{1\over2}$$
)
(12,
$$2{1\over2}$$
)
(17, 4)
(16,
$$4{1\over4}$$
)
[IMG]


correct_option_index: 3